The prediction theory of multivariate stochastic processes, III
The prediction theory of multivariate stochastic processes, III
复制标题
多元随机过程的预测理论，III
DOI：
10.1007/bf02547188
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发表时间：
1960
期刊：
影响因子：
3.7
通讯作者：
P. Masani
中科院分区：
文献类型：
--
作者：
P. Masani
本文将证明Wiener和作者在[8]中得到的确定q变量、离散参数、弱平稳随机过程（SP）的母函数和预报误差矩阵的算法，以及线性预报器在时域上的唯一的、均值收敛的、自回归的序列。（2）在谱密度矩阵F ′的特征值有界于零上的情况下，在更一般的情况下是有效的。在F '的最大特征值与最小特征值之商在L1中，F'可逆ae，F '-1EL1的较弱条件下，证明了该算法是成立的。在假设F ′ EL ~，F ′-1 EL ~ 1下，预测因子的序列将被证明是占优势的，该假设虽然比最后一个更严格，但也比II中假设的弱。
We shall show that the algorithm for determining the generating function and prediction error matrix of a q-variate, discrete parameter, weakly stationary, stochastic process (SP), as well as the unique, mean-convergent, autoregressive series for the linear predictor in the time-domain, which were obtained by Wiener and the writer in [8, Part II](2) in case the eigenvalues of the spectral density matrix F'are bounded above and away from zero, are valid under a more general setting. The algorithm will be shown to hold under the weaker conditions that the quotient of the largest to the smallest eigenvalue of F'is in L1, F'is invertible ae and F'-1 EL 1. The series for the predictor will be shown to prevail under the hypothesis F'EL~, F'-1 EL 1, which while more stringent than the last is again weaker than that assumed in II.